Ground-State Structure in $\nu =2$ Bilayer Quantum Hall Systems

We investigate the ground-state structure of the bilayer quantum Hall system at the filling factor $\nu =2$. Making an exact analysis of the ground state in the SU(4)-invariant limit, we include all other interactions as small perturbation. We carry out analytic calculations and construct phase diagrams for nonzero values of the Zeeman, tunneling and bias interactions. In particular we examine carefully how the phase transition occurs by applying the bias voltage and inducing a density imbalance between the two layers. We compare our theoretical result with the experimental data due to Sawada et al. based on the phase diagram in the $\sigma_{0}$-$\rho_{0}$ plane, where $\rho _{0}$ and $\sigma_{0}$ are the total electron density and the density difference between the two layers, respectively.